There are several synonyms that can be used instead of the phrase "with downcast eyes." One option is "with averted gaze," which implies a deliberate avoidance of eye contact. Another alternative is "with bowed head," which suggests a show of deference or humility. "Looking dejected" conveys a sense of sadness or defeat, while "sulking" suggests resentment or displeasure. "Shamefaced" implies embarrassment or guilt, while "crestfallen" indicates disappointment or discouragement. Ultimately, the choice of synonym will depend on the context and tone of the sentence, but there are many options that can help convey the desired emotion or attitude.